Blender subdividing faces and creating edges where shouldn't be any
The face where you are seeing that extra fold is twisted, its top edge is rotated from its bottom edge. So it isn't possible to render it with flat shading, and Blender thus calculated a bend there.

To avoid this, turn on smooth shading on the object - in object mode, press T while in the 3d viewer to open the toolbar, then go to the Shading section under Tools > Transform, and click the Smooth Button.



Then add an Edge Split modifier to the object. 



The extra edge is now gone.